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Introduction to Corporate Finance

- Chapter 1

Corporate Finance addresses the following three

questions

- What long-term investments should the firm

choose? - How should the firm raise funds for the selected

investments? - How should short-term assets be managed and

financed?

Balance Sheet Model of the Firm

The Capital Budgeting Decision

Current Liabilities

Current Assets

Long-Term Debt

Fixed Assets 1 Tangible 2 Intangible

Shareholders Equity

What long-term investments should the firm choose?

The Capital Structure Decision

Current Liabilities

Current Assets

Long-Term Debt

How should the firm raise funds for the selected

investments?

Fixed Assets 1 Tangible 2 Intangible

Shareholders Equity

Short-Term Asset Management

Current Liabilities

Current Assets

Net Working Capital

Long-Term Debt

- How should short-term assets be managed and

financed?

Fixed Assets 1 Tangible 2 Intangible

Shareholders Equity

Capital Structure

The value of the firm can be thought of as a pie.

Capital Structure

The value of the firm can be thought of as a pie.

The goal of the manager is to increase the size

of the pie. Where should the firm invest?

Capital Structure

The value of the firm can be thought of as a pie.

The goal of the manager is to increase the size

of the pie. Where should the firm invest?

Capital Structure decision can be viewed as how

the pie is sliced. How do we raise funds?

The Financial Manager

- The Financial Managers primary goal is to

increase the value of the firm by - Selecting value creating projects
- Capital Budgeting Decision
- Making smart financing decisions
- Capital Structure Decision

The Firm and the Markets

Firm issues securities

Retained cash flows

Investsin assets(B)

Cash flowfrom firm

Div and debt payments

Short-term debt Long-term debt Equity shares

Current assetsFixed assets

Taxes

The cash flows from the firm must exceed the cash

flows from the financial markets.

Ultimately, the firm must be a cash generating

activity.

1.2 Forms of Business Organization

- The Sole Proprietorship
- The owner of the firm also runs the firm
- The Partnership
- General Partnership
- Like a sole proprietorship, but with several

owners - Limited Partnership
- Some partner bears limited financial risk, and do

not participate in running the company - The Corporation
- Generally used when need to raise a large amount

of capital - Separates ownership and control

A Comparison

1.3 The Goal of Financial Management

- What is the correct goal?
- Maximize profit?
- Minimize costs?
- Maximize market share?
- Maximize shareholder wealth?

1.4 The Agency Problem

- Agency relationship
- Principal hires an agent to represent his/her

interest - Stockholders (principals) hire managers (agents)

to run the company - Other Ex. Real Estate Agents, Mutual Funds
- Agency problem
- Conflict of interest between principal and agent
- Agents goals may not be the same as Principals

Managerial Goals

- Managerial goals may be different from

shareholder goals - Expensive perquisites
- Private jet, golf memberships, cars, etc.
- Company Survival,
- Independence

Managing Managers

- Managerial compensation
- Incentives are used to align management and

stockholder interests - Ex. Stock Options, Performance Bonuses
- The incentives need to be structured carefully to

make sure that they achieve their intended goal - Corporate control
- The threat of a takeover force managers to act in

stockholder interest

1.5 Financial Markets

- Primary Market
- Issuance of a security for the first time
- Secondary Markets
- Buying and selling of previously issued

securities - Securities may be traded in either a dealer or

auction market - Some Financial Markets NYSE, NASDAQ, London

Tokyo Stock Exchanges

Financial Markets

Investors

Firms

Sue

Bob

Quick Quiz

- What are the three basic questions Financial

Managers must answer? - What are the three major forms of business

organization? - What is the goal of financial management?
- What are agency problems, and why do they exist

within a corporation? - What is the difference between a primary market

and a secondary market?

Financial Statements and Cash Flow

- Chapter 2

2.1 The Balance Sheet

- A snapshot of the firms accounting value at a

specific point in time - What does the company look like today
- The Balance Sheet Identity is
- Assets Liabilities Stockholders Equity
- Left Hand Side of the balance sheet must equal

the Right Hand Side

Balance Sheet

U.S. Composite Corporation Balance Sheet

The assets are listed in order by the length of

time it would normally take a firm with ongoing

operations to convert them into cash. Clearly,

cash is much more liquid than property, plant,

and equipment.

2007

2006

Current Liabilities

Accounts payable

213

197

Notes payable

50

53

Accrued expenses

223

205

Total current liabilities

486

455

Long-term liabilities

Deferred taxes

117

104

Long-term debt

471

458

Total long-term liabilities

588

562

Stockholder's equity

Preferred stock

39

39

Common stock (1 per value)

55

32

Capital surplus

347

327

Accumulated retained earnings

390

347

Less treasury stock

(26)

(20)

Total equity

805

725

Total liabilities and stockholder's equity

1,879

1,742

Balance Sheet Analysis

- When analyzing a balance sheet, the Finance

Manager should be aware of three concerns - Liquidity
- Debt versus Equity
- Value versus Cost

Liquidity

- Refers to the ease and quickness with which

assets can be converted to cashwithout a

significant loss in value - Generally the more liquid the asset the lower the

rate of return - Current assets are more liquid than fixed assets
- The more liquid a firms assets, the less likely

the firm is to experience problems meeting

short-term cash obligations (Ex. payroll)

Debt versus Equity

- Debt ? Liability
- Promise to payout cash, an IOU
- Equity is the residual
- Assets Liabilities Equity
- Debt represents a senior claim on firm assets
- If the firm goes bankrupt debt holders get paid

before equity holders

Value versus Cost

- Accountants are historians, they care about what

something cost when purchase - Under GAAP, financial statements carry assets at

cost - Market value is the price at which assets,

liabilities, and equity could actually be bought

or sold, TODAY - Cost and Market Value are two completely

different concepts - What did we pay for it, versus what can we sell

it for

2.2 The Income Statement

- Measures financial performance over a specific

period of time - How has the company performed?
- The accounting definition of income is
- Revenue Expenses Income
- Generally the Income Statement is comprised of

several parts

U.S.C.C. Income Statement

Total operating revenues

2,262

The operations section of the income statement

reports the firms revenues and expenses from

principal operations.

Cost of goods sold

1,655

Selling, general, and administrative expenses

327

Depreciation

90

Operating income

190

Other income

29

Earnings before interest and taxes

219

Interest expense

49

Pretax income

170

Taxes

84

Current 71

Deferred 13

Net income

86

U.S.C.C. Income Statement

Total operating revenues

2,262

The non-operating section of the income statement

includes all financing costs, such as interest

expense.

Cost of goods sold

1,655

Selling, general, and administrative expenses

327

Depreciation

90

Operating income

190

29

Other income

Earnings before interest and taxes

219

Interest expense

49

Pretax income

170

Taxes

84

Current 71

Deferred 13

Net income

86

U.S.C.C. Income Statement

Total operating revenues

2,262

Cost of goods sold

1,655

Selling, general, and administrative expenses

327

Depreciation

90

Operating income

190

Other income

29

Earnings before interest and taxes

219

Usually a separate section reports the amount of

taxes levied on income.

Interest expense

49

Pretax income

170

Taxes

84

Current 71

Deferred 13

Net income

86

U.S.C.C. Income Statement

Total operating revenues

2,262

Cost of goods sold

1,655

Selling, general, and administrative expenses

327

Depreciation

90

Operating income

190

Other income

29

Earnings before interest and taxes

219

Interest expense

49

Net income is the bottom line.

Pretax income

170

Taxes

84

Current 71

Deferred 13

Net income

86

Income Statement Analysis

- There are three things to keep in mind when

analyzing an income statement - Generally Accepted Accounting Principles (GAAP)
- Non-Cash Items
- Time and Costs

GAAP

- The matching principal of GAAP dictates that

revenues be matched with expenses. - Thus, income is reported when it is earned, even

though no cash flow may have occurred.

Non-Cash Items

- The income statements also makes allowances for

expense where no money changes hands - Depreciation is the most apparent example. No

firm ever writes a check for depreciation. - Another non-cash item is deferred taxes, which

does not represent a cash flow. - Thus, net income is not cash.

Time and Costs

- In the short-run, certain equipment, resources,

and commitments of the firm are fixed, but the

firm can vary such inputs as labor and raw

materials. - In the long-run, all inputs of production (and

hence costs) are variable. - Financial accountants do not distinguish between

variable costs and fixed costs. Instead,

accounting costs usually fit into a

classification that distinguishes product costs

from period costs.

2.3 Taxes

- In this world nothing is certain but death and

taxes. Ben Franklin - Taxes represent a major cost to the firm
- Taxes rules change, and are subject to political,

not economic forces - What this means is that taxes do not need to make

economic sense - Company is subject to two different tax rates
- Marginal the percentage paid on the next dollar

earned - Average the tax bill / taxable income

Marginal versus Average Rates

- Suppose your firm earns 4 million in taxable

income. - What is the firms tax liability?
- .15(50,000) .25(75,000 50,000) .34(100,000

75,000) .39(335,000 100,000)

.34(4,000,000 335,000) 1,356,100 - Rate from table 2.3
- What is the average tax rate?
- What is the marginal tax rate?
- If you are considering a project that will

increase the firms taxable income by 1 million,

what tax rate should you use in your analysis?

2.4 Net Working Capital

- Net Working Capital (NWC)
- Current Assets Current Liabilities
- NWC is usually positive for a growing firm
- Why?

U.S.C.C. Balance Sheet

2.5 Financial Cash Flow

- As finance people what we are really interested

in is the firms actual cash flow - Since there is no magic in finance, it must be

the case that the cash flow received from the

firms assets must equal the cash flows to the

firms creditors and stockholders. - CF(A) CF(B) CF(S)

U.S.C.C. Financial Cash Flow

Cash Flow of the Firm

Operating cash flow

238

(Earnings before interest and taxes

plus depreciation minus taxes)

Capital spending

-173

(Acquisitions of fixed assets

minus sales of fixed assets)

Additions to net working capital

-23

Total

42

Cash Flow of Investors in the Firm

Debt

36

(Interest plus retirement of debt

minus long-term debt financing)

Equity

6

(Dividends plus repurchase of

equity minus new equity financing)

Total

42

2.5 The Statement of Cash Flows

- There is a third accounting statement called the

statement of cash flows. - The three components are
- Cash flow from operating activities
- Cash flow from investing activities
- Cash flow from financing activities

U.S.C.C. Cash Flow from Operations

To calculate cash flow from operations, start

with net income, add back non-cash items like

depreciation and adjust for changes in current

assets and liabilities (other than cash).

U.S.C.C. Cash Flow from Investing

Cash flow from investing activities involves

changes in capital assets acquisition of fixed

assets and sales of fixed assets (i.e., net

capital expenditures). The cash from sales of

our buildings/machinery minus the cost of

buildings/machinery we bought

U.S.C.C. Cash Flow from Financing

Cash flows to and from creditors and owners

include changes in equity and debt.

U.S.C.C. Statement of Cash Flows

The statement of cash flows is the addition of

cash flows from operations, investing, and

financing.

Quick Quiz

- What is the difference between book value and

market value? Which should we use for decision

making purposes? - What is the difference between accounting income

and cash flow? Which do we need to use when

making decisions? - What is the difference between average and

marginal tax rates? Which should we use when

making financial decisions? - How do we determine a firms cash flows? What are

the equations, and where do we find the

information?

Financial Statements Analysis and Long-Term

Planning

- Chapter 3

3.1 Financial Statements Analysis

- Common-Size Balance Sheets
- Compute all accounts as a percent of total assets
- Common-Size Income Statements
- Compute all line items as a percent of sales
- Standardized statements make it easier to compare

financial information, particularly as the

company grows. - They are also useful for comparing companies of

different sizes, particularly within the same

industry.

3.2 Ratio Analysis

- Ratios allow for a better comparison through time

and/or between companies - Give a sense for how the firm is doing
- As we look at each ratio, ask yourself
- How is the ratio computed?
- What is the ratio trying to measure and why?
- What is the unit of measurement?
- What does the value indicate?
- How can we improve the companys ratio?

Categories of Financial Ratios

- Short-term solvency, or liquidity ratios
- Long-term solvency, or financial leverage ratios
- Asset management, or turnover ratios
- Profitability ratios
- Market value ratios

Liquidity Ratios

- These measure the ability of the firm to meet

its short term obligations - Why is this important?
- Current Ratio CA / CL
- 708 / 540 1.31 times
- Quick Ratio (Acid Test) (CA Inventory) / CL
- (708 - 422) / 540 0.53 times
- Cash Ratio Cash / CL
- 98 / 540 0.18 times
- Where do the raw numbers come from?

Leverage Ratios

- These measure the ability of the firm to meet

its long term obligations - Why is this important?
- Total Debt Ratio (TA TE) / TA
- (3588 - 2591) / 3588 28
- Debt/Equity TD / TE
- (3588 2591) / 2591 38.5
- Equity Multiplier TA / TE 1 D/E
- 1 .385 1.385
- Where do the raw numbers come from?

Coverage Ratios

- These measure the ability of the firm to pay its

debt holders - Why do we care about paying the debt holders?
- Times Interest Earned EBIT / Interest
- 691 / 141 4.9 times
- Cash Coverage (EBIT Depreciation) / Interest
- (691 276) / 141 6.9 times
- Where do the raw numbers come from?

Inventory Ratios

- These tell else how efficiently the firm manages

its inventory - Why do we care about this?
- Do we want these ratios to be high or low?
- Where do the raw numbers come from?
- Inventory Turnover Cost of Goods Sold /

Inventory - 1344 / 422 3.2 times
- Days Sales in Inventory 365 / Inventory

Turnover - 365 / 3.2 114 days

Receivables Ratios

- These tell else how quickly the firm is paid?
- Why do we care about this?
- Do we want these ratios to be high or low?
- Where do the raw numbers come from?
- Receivables Turnover Sales / Accounts

Receivable - 2311 / 188 12.3 times
- Days Sales in Receivables 365 / Receivables

Turnover - 365 / 12.3 30 days

Total Asset Turnover

- This tells us how efficiently the firm is turning

assets into sales - Why do we care about this?
- Total Asset Turnover Sales / Total Assets
- 2311 / 3588 0.64 times
- It is not unusual for TAT lt 1, especially if a

firm has a large amount of fixed assets.

Profitability Measures

- These measure how efficiently the firm operates
- Why do we care about these?
- Where do the raw numbers come from?
- Profit Margin Net Income / Sales
- 363 / 2311 15.7
- Return on Assets (ROA) Net Income / Total

Assets - 363 / 3588 10.1
- Return on Equity (ROE) Net Income / Total

Equity - 363 / 2591 14.0

Market Value Measures

- These tell us how the market (people) feel about

the firm - Where do these raw numbers come from?
- Market Price 88 per share
- Shares outstanding 33 million
- PE Ratio Price per share / Earnings per share
- 88 / 11 8 times
- Market-to-book ratio market value per share /

book value per share - 88 / (2591 / 33) 1.12 times

3.3 The Du Pont Identity

- Breaking down ROE into it component parts
- ROE NI / TE
- Multiply by 1 and then rearrange
- ROE (NI / TE) (TA / TA)
- ROE (NI / TA) (TA / TE) ROA EM
- Multiply by 1 again and then rearrange
- ROE (NI / TA) (TA / TE) (Sales / Sales)
- ROE (NI / Sales) (Sales / TA) (TA / TE)
- ROE PM TAT EM

What does it mean?

- ROE PM TAT EM
- Profit margin is a measure of the firms

operating efficiency how well it controls

costs. - Total asset turnover is a measure of the firms

asset use efficiency how well it manages its

assets. - Equity multiplier is a measure of the firms

financial leverage.

The Du Pont Identity in action

- ROA 10.1 and EM 1.39
- ROE 10.1 1.385 14.0
- PM 15.7 and TAT 0.64
- ROE 15.7 0.64 1.385 14.0

3.4 Using Financial Statements

- Ratios are not very helpful by themselves they

need to be compared to something - Time-Trend Analysis
- Used to see how the firms performance is

changing through time - Peer Group Analysis
- Compare to similar companies or within industries
- SIC and NAICS codes

Potential Problems to Remember when Analyzing

Financial Statement

- There is no underlying theory, so there is no

definitive way to know which ratios are most

relevant - Benchmarking is difficult
- Especially for diversified firms
- Firms use varying accounting procedures
- Ex. LIFO versus FIFO
- Globalization means different accounting

regulations - Firms have different fiscal years
- Extraordinary, or one-time, events

3.5 Long-Term Financial Planning

- These are the big decisions
- Planning where the company is heading
- Investment in new assets (Capital budgeting

decisions) - Does Nike start a magazine?
- Degree of financial leverage (Capital structure

decisions) - Should we issue more bonds?
- Generally we make these decisions based on pro

forma financial statement

Percent of Sales Approach

- Relatively quick and simple way to generate pro

forma financial statements - Which can also be used to estimate where the

company is heading - Remember that some items vary directly with

sales, while others do not - Costs may vary directly with sales
- Depreciation and interest expense generally do

not vary directly with sales - Dividends are a management decision and generally

do not vary directly with sales

Pro Forma Income Statement

3.6 External Financing and Growth

- At low growth levels, internal financing

(retained earnings) may exceed the required

investment in assets. - As the growth rate increases, the internal

financing will not be enough, and the firm will

have to go to the capital markets for financing. - Examining the relationship between growth and

external financing required is a useful tool in

long-range planning.

The Internal Growth Rate

- The internal growth rate tells us how fast the

firm can grow assets using only retained earnings

for financing - The Internal Growth Rate can be calculated with

ROA and Plowback - Plowback ratio how much of net income is being

reinvested in the company - b Addition to Retained Earnings / Net Income

Calculating the Internal Growth Rate

- Using the information from the Hoffman Co.
- ROA 66 / 500 0.132
- b 44/ 66 .66700
- Internal Growth Rate
- (ROA b )/ (1 ROA b)
- (0.132 0.667) / (1 0.132 0.667 ) 0.0965
- Hoffman Co. can grow at 9.65 using only internal

funds

The Sustainable Growth Rate

- The sustainable growth rate tells us how fast the

firm can grow by using internally generated funds

and issuing debt, without changing the firms

leverage - Do you expect this be higher or lower than the

internal growth rate? - The Sustainable Growth Rate can be calculated

with ROE and Plowback

Calculating the Sustainable Growth Rate

- Using the Hoffman Co.
- ROE 66 / 250 0.264
- b 0.667
- Sustainable Growth Rate
- (ROE b )/ (1 ROE b)
- (0.264 0.667) / (1 0.264 0.667 ) 0.214
- Hoffman Co. can grow at 21.4 using only internal

funds

Determinants of Growth

- Profit margin operating efficiency
- Total asset turnover asset use efficiency
- Financial leverage choice of optimal debt ratio
- Dividend policy choice of how much to pay to

shareholders versus reinvesting in the firm

3.7 Some Caveats

- Financial planning models do not indicate which

financial polices are the best. - Models are simplifications of reality, and the

world can change in unexpected ways. - Without some sort of plan, the firm may find

itself adrift in a sea of change without a rudder

for guidance.

Quick Quiz

- How do you standardize balance sheets and income

statements? - Why is standardization useful?
- What are the major categories of financial

ratios? - How do you compute the ratios within each

category? - What are some of the problems associated with

financial statement analysis?

Quick Quiz

- What is the purpose of long-range planning?
- What are the major decision areas involved in

developing a plan? - What is the percentage of sales approach?
- What is the internal growth rate?
- What is the sustainable growth rate?
- What are the major determinants of growth?

Discounted Cash Flow Valuation

- Chapter 4

BASIC PRINCIPAL

- Is a dollar today worth more or less than a

dollar in 30 years? - Why?
- Or would you rather have 1,000 today or 1,000

in 30 years? - FYI this is one of those fundamental building

blocks of finance

Present Value

- Present Value is the value of a future payment

today - Find this by discounting
- In order to find the present value, we need to

know the discount rate, r - Also know as the hurdle rate or the opportunity

cost of capital

One Period Discounting

- PV Future Value / (1 Discount Rate)
- V0 C1 / (1r)
- Alternatively
- PV Future Value Discount Factor
- V0 C1 (1/ (1r))
- Discount factor is 1/ (1r)

PV Example

- What is the value today of 100 in one year, if

r15?

Future Value

- In the one-period case, the formula for FV can be

written as - FV C0(1 r)
- Where C0 is cash flow today (time zero), and
- r is the appropriate discount rate.

FV Example

- What is the value in one year of 100, invested

today at 15?

NPV

- NPV Present Value of all expected cash flows
- Represents how much value the project is

contributing to the firm - To compute NPV we need to know two components

appropriate discount rate and the expected cash

flows (timing and magnitude).

Net Present Value (NPV)

- NPV PV (Costs) PV (Benefit)
- Costs are negative cash flows
- Benefits are positive cash flows
- One period example
- NPV C0 C1 / (1r)
- For investments C0 will be negative, and C1 will

be positive - Reverse for loan

Net Present Value Example

- Suppose you can buy an investment that promises

to pay 10,000 in one year for 9,500. Should you

invest?

Net Present Value

- We cannot simply compare the two cash flows
- They occur at different times
- We need to find the NPV of the investment
- If the NPV is positive then we buy
- Your interest rate is 5.
- NPV
- At what price are we indifferent?

Coffee Shop Example

- If you build a coffee shop on campus, you can

sell it to Starbucks in one year for 300,000 - Costs of building a coffee shop is 275,000
- Should you build the coffee shop?

Step 1 Draw it out

Step 2 Discount Rate

- Assume that the Starbucks offer is guaranteed
- US T-Bills are risk-free and currently pay 7

interest - This is known as rf
- Thus, the appropriate discount rate is 7
- Why

Example Continues

- Step 3 Find the present value of future cash

flows, our money from Starbucks - Step 4 Use the NPV rule
- So do we build or not?

If we are unsure about future?

- Is the appropriate discount rate
- rd rf
- rd gt rf
- rd lt rf

Note on Discount Rates

- The discount rate should take into account
- Time value of money
- Riskiness of cash flow
- The appropriate discount rate is the opportunity

cost of capital - The opportunity cost of capital is the rate of

return offered by comparable investment

opportunities.

Risky Coffee Shop

- Assume that the risk of the coffee shop is

equivalent to an investment in the stock market

which is currently paying 12 - Should we still build the coffee shop?

Calculations?

- Need to recalculate PV and NPV
- PV
- NPV
- Does the project still add value?

Expected Cash Flows

- Future cash flows are generally not certain
- Therefore need to form expectations
- Need to identify the factors that affect cash

flows (ex. Weather etc). - Determine the various scenarios for this factor

(ex. rainy or sunny) - Estimate cash flows under the various scenarios

(sensitivity analysis) - Assign probabilities to each scenario

Expectation Calculation

- Expected value of X is the weighted sum of the

possible values of X where the weight is given by

the probability of its occurrence, p. - E(X) p1X1 p2X2 . psXs
- E(X) p1X1 p2X2 . psXs
- E(X) Expected Value of X
- Xi ? Outcome of X in state i
- pi Probability of state i
- s Number of possible states
- Note that p1 p2 . ps 1

Dice Example

- What is the expected value of the role of a dice?
- What are the possible states?
- What is the probability of anyone state occurring?

Coffee Shop Expected Future Value

- If the value of the coffee shop depends on the

state of the economy, what is the expected future

value?

Calculations

- Discount Rate 12
- Expected Future Cash Flow
- NPV
- Do we still build the coffee shop?

Valuing a Project Summary

- Step 1 Forecast cash flows
- Step 2 Draw out the cash flows
- Step 3 Determine the opportunity cost of

capital - Step 4 Discount future cash flows
- Step 5 Apply the NPV rule

Reminder

- Important to set up problem correctly
- Keep track of
- Magnitude and timing of the cash flows
- TIMELINES
- You cannot compare cash flows _at_ t3 and _at_ t2 if

they are not in present value terms!!

Discounted Cash Flow Analysis

- A method of evaluating an investment by

estimating future cash flows and taking into

consideration the time value of money - Provides us with the present value of the

investment (NPV) - This allows for the comparison of investments
- If capital is limited allows for the selection of

the more valuable investment

General Formula

- PV0 FVN/(1 r)N OR FVN PVo(1 r)N
- Given any three, you can solve for the fourth
- Present value (PV)
- Future value (FV)
- Time period
- Discount rate

Four Related Questions

- How much must you deposit today to have 1

million in 25 years? (r12) - If a 58,823.31 investment yields 1 million in

25 years, what is the rate of interest? - How many years will it take 58,823.31 to grow to

1 million if r12? - What will 58,823.31 grow to after 25 years if

r12?

FV Example

- Suppose a stock is currently worth 10, and is

expected to grow at 40 per year for the next

five years. - What is the stock worth in five years?

PV Example

- How much would an investor have to set aside

today in order to have 20,000 five years from

now if the current rate is 15?

20,000

PV

Simple vs. Compound Interest

- Simple Interest Where interest accumulates only

on the principal - Compound Interest Where interest is accumulated

on the principal as well as the interest already

accumulated - What will 100 grow to after 2 periods at 10?
- Compounded interest
- FV2 PV0 (1r) (1r) PV0 (1r)2
- Simple interest
- FV2 (PV0 (r) PV0 (r)) PV0 PV0 (1 2r)

Compounding Periods

- We have been assuming that compounding and

discounting occurs annually, this does not need

to be the case

Non-Annual Compounding

- Cash flows are usually compounded over periods

shorter than a year - The relationship between PV FV when interest is

not compounded annually for N years - FVN PV ( 1 r / M) MN
- PV FVN / ( 1 r / M) MN
- M is number of compounding periods per year

Compound Interest

Interest Rates

- In the table the 6 interest is known as the

Stated Annual Interest Rate (more popularly known

as the Annual Percentage Rate) - This is the rate that will generally be quoted
- Ex Car loan, mortgage
- However, this does not tell us the interest rate

earned on our investment over the year - The interest rate that the investment actually

earns over the year, is the Effective Annual Rate

Continuous Compounding

- The general formula for the future value of an

investment compounded continuously over many

periods can be written as - FV C0erT
- e is a transcendental number approximately equal

to 2.718. ex is a key on your calculator. - Example The future value of 100 continuously

compounded at 10 for one year is 100e.10

110.52

Power of compounding

Compounding Example

- What is the FV of 500 in 5 years, if the

discount rate is 12, compounded monthly? - FV
- What is the PV of 500 received in 5 years, if

the discount rate is 12 compounded monthly? - PV

Compounding Example 2

- If you invest 50 for 3 years at 12 compounded

semi-annually, your investment will grow to

___________

Alternative Calculating the EAR

- EAR (1 R/m)m 1
- Earlier example 12 semi-annual
- EAR
- Using the EAR
- FV
- So, investing at _____ compounded annually is

the same as investing at 12 compounded

semi-annually.

EAR Example

- Find the Effective Annual Rate (EAR) of an 18

APR loan that is compounded weekly. - EAR

Present Value Of a Cash Flow Stream

- The present value of a stream of cash flows can

be found using the following general valuation

formula. - In other words, discount each cash flow back to

the present using the appropriate discount rate

and then sum the present values.

Insight Example

Which project is more valuable? Why?

Example (Given)

- Consider an investment that pays 200 one year

from now, with cash flows increasing by 200 per

year through year 4. If the interest rate is 12,

what is the present value of this stream of cash

flows? - If the issuer offers this investment for 1,500,

should you purchase it?

Multiple Cash Flows (Given)

0

1

2

3

4

200

400

600

800

178.57

318.88

427.07

508.41

1,432.93

Common Cash Flows

- Perpetuity, Growing Perpetuity
- A constant stream of cash flows that lasts

forever - A stream of cash flows that grows at a constant

rate forever - Annuity, Growing Annuity
- A stream of constant cash flows that lasts for a

fixed number of periods - A stream of cash flows that grows at a constant

rate for a fixed number of periods - All of the following formulas assume the first

payment is next year, and payments occur annually

Perpetuity

- A constant stream of cash flows that lasts

forever - Since we arent able to spend forever calculating

a perpetuitys PV - PVC/r
- What is PV if C100 and r10

Growing Perpetuities

- Annual payments grow at a constant rate, g
- PV C1/(1r) C1(1g)/(1r)2 C1(1g)2(1r)3
- PV C1/(r-g)
- What is PV if C100, r10, and g2?

Growing Perpetuity Example (Given)

- The expected dividend next year is 1.30, and

dividends are expected to grow at 5 forever. - If the discount rate is 10, what is the value of

this promised dividend stream?

1.30 (1.05)2 1.43

1.30(1.05) 1.37

2

3

- PV 1.30 / (0.10 0.05) 26

Example

- An investment in a growing perpetuity costs
- 5,000 and is expected to pay 200 next year.
- If the interest is 10, what is the growth rate
- of the annual payment?

Annuity

- A constant stream of cash flows with a fixed

maturity

Annuity Example 1

- Compute the present value of a 3 year ordinary

annuity with payments of 100 at r10 - Answer

An Alternative to the Formulas, is a Financial

Calculator

- Texas Instruments BA-II Plus, basic
- N number of periods
- I/Y periodic interest rate
- P/Y must equal 1 for the I/Y to be the periodic

rate - Interest is entered as a percent, not a decimal
- PV present value
- PMT payments received periodically
- FV future value
- Remember to clear the registers (CLR TVM) after

each problem - Other calculators are similar in format

Annuity Example 2

- You agree to lease a car for 4 years at 300 per

month. You - are not required to pay any money up front or at

the end of - your agreement. If your opportunity cost of

capital is 0.5 - per month, what is the cost of the lease?
- Work through on financial calculators

Annuity Example 3

- What is the value today of a 10-year annuity that

pays 600 every other year? Assume that the

stated annual discount rate is 10. - What do the payments look like?
- What is the discount rate?

Annuity Example 4

- What is the present value of a four-year annuity

of 100 per year that makes its first payment two

years from today if the discount rate is 9?

Annuity Example 5

- What is the value today of a 10-pymt annuity that

pays 300 a year (at year-end) if the annuitys

first cash flow is at the end of year 6. The

interest rate is 15 for years 1-5 and 10

thereafter? - Steps
- Get value of annuity at t 5 (year end)
- Bring value in step 1 to t0

Delayed first payment Perpetuity

- What is the present value of a growing

perpetuity, that pays 100 per year, growing at

6, when the discount rate is 10, if the first

payment is in 12 years?

Growing Annuity

- A growing stream of cash flows with a fixed

maturity

Growing Annuity Example

- A defined-benefit retirement plan offers to pay

20,000 per year for 40 years and increase the

annual payment by 3 each year. What is the

present value at retirement if the discount rate

is 10?

Growing Annuity Example (Given)

You are evaluating an income generating property.

Net rent is received at the end of each year. The

first year's rent is expected to be 8,500, and

rent is expected to increase 7 each year. What

is the present value of the estimated income

stream over the first 5 years if the discount

rate is 12? PV (8,500/(.12-.07)) 1-

1.07/1.125 34,706.26

Valuation Formulas

Remember

- That when you use one of these formulas or the

calculator the assumptions are that - PV is right now, and the first payment is next

year

What Is a Firm Worth?

- A firm is worth the present value of the firms

cash flows. - PV (Equity) PV of their expected cash flows
- PV (Debt) PV of their expected cash flows
- The tricky part is determining the size, timing,

and risk of those cash flows.

Quick Quiz

- How is the future value of a single cash flow

computed? - How is the present value of a series of cash

flows computed. - What is the Net Present Value of an investment?
- What is an EAR, and how is it computed?
- What is a perpetuity? An annuity?

Why We Care

- The Time Value of Money is the basic foundation

of knowledge that people will assume that you know

How to Value Bonds and Stocks

- Chapter 5

What is a Bond?

- A bond is a legally binding agreement between a

borrower and a lender - IOU

Bond Terminology

- Face value (F) or Principal
- For a corporate bond this is generally 1,000
- Coupon rate
- This is a Stated Annual rate
- However, coupons are generally paid semi-annually
- Coupon payment (C )
- Zero- coupon bond
- Yield to maturity
- Rating

Yield to Maturity

- YTM is the interest that the bond is offering at

its current price, if held till maturity - R for the previous slide
- It is determined by
- Time to maturity
- Longer term bonds should have higher yields
- Risk of default
- Risk is measured by bond ratings

Valuing a Bond

- The value of a bond is just the present value of

its future cash flows - Bonds are valued like a package of two

investments - Present value of the coupon (interest) payments
- Present value of the principal payment

Pure Discount Bonds

- This is a bond that makes no coupon payments
- Sometimes called zeroes, deep discount bonds, or

original issue discount bonds (OIDs) - Example T-Bill
- Yield to maturity (return) comes only from the

difference between the purchase price and face

(par) value - A pure discount bond cannot sell for more than

par value. WHY?

Pure Discount Bonds

- Information needed for valuing pure discount

bonds - Time to maturity (T) Maturity date - todays

date - Face value (F)
- Discount rate (r)

Present value of a pure discount bond at time 0

Pure Discount Bond Example

- Find the value of a 30-year zero-coupon bond with

a 1,000 par value and a YTM of 6.

Coupon Bonds

- Make periodic coupon payments in addition to the

principal value - The coupon payments are the same each period.
- Coupon payments are typically semi-annual.
- Effective annual rate
- EAR (1 R/m)m 1
- The bond is just a combination of an annuity and

a terminal (maturity) value.

Coupon Bond Pricing Equation

- Simply an annuity with a lump sum payment at the

end

Coupon Bond Pricing BA II plus

- N This is the number of coupon payments
- I/Y This is the rate discount rate for the

coupon period - PV The price of the bond today
- PMT this is the amount of the coupon payment
- FV This is the principal that will be repaid

Valuing a Corporate Bond

- Dupont issued a 30 year maturity bonds with a

coupon rate of 7.95. - Interest is paid semi-annually
- These bonds currently have 28 years remaining to

maturity and are rated AA. - The bonds have a par value of 1,000
- Newly issued AA bonds with maturities greater

than 10 years are currently yielding 7.73 - What is the value of Dupont bond today?

Dupont example (continued)

- Annual interest ()
- Semiannual coupon payment
- Semiannual discount rate
- Number of semiannual periods
- PV

Level Coupon Bond Example (Given)

- Consider a U.S. government bond with a 6 3/8

coupon that expires in December 2010. - The Par Value of the bond is 1,000.
- Coupon payments are made semi-annually (June 30

and December 31 for this particular bond). - Since the coupon rate is 6 3/8, the payment is

31.875. - On January 1, 2006 the size and timing of cash

flows are - The require annual rate is 5

Level Coupon Bond Example (Given)

- Coupon Rate 6 3/8, pay semi-annually
- 10 Semi-Annual Payments of 31.875.
- Maturity December 2010, Start Jan. 2006
- The Par Value of the bond is 1,000.
- The require annual rate is 5
- N 10, I/Y 2.5, PV???, PMT 31.875,

FV1,000 PV 1,060.17

Valuing a Corporate Bond (Given)

- Value a bond with the following characteristics

(calculator) - Face value 1,000
- Coupon rate (C ) 8
- Time to maturity 4 years
- Discount rate 9
- Present Value 967.02
- You should know how to get any one of these

numbers given the other 4.

YTM and bond prices

- When coupon rate YTM, price par value
- When coupon rate gt YTM, price gt par value

(premium bond) - When coupon rate lt YTM, price lt par value

(discount bond) - What will a zero sell at?
- Bond prices and market interest rates move in

opposite directions.

YTM and Bond Value

When the YTM lt coupon, the bond trades at a

premium.

1300

1200

Bond Value

When the YTM coupon, the bond trades at par.

1100

1000

800

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

Discount Rate

Coupon Rate

When the YTM gt coupon, the bond trades at a

discount.

Computing Yield to Maturity

- Finding the YTM requires trial and error if you

do not have a financial calculator - If you have a financial calculator, enter N, PV,

PMT, and FV, remembering the sign convention - PMT and FV need to have the same sign, PV the

opposite sign

YTM with Semiannual Coupons

- Suppose a bond with a 10 coupon rate and

semiannual coupons has a face value of 1,000, 20

years to maturity, and is selling for 1,197.93. - Is the YTM more or less than 10?
- What is the semi-annual coupon payment?
- How many periods are there?
- What is the YTM?

YTM with Annual Coupons (Given)

- Consider a bond with a 10 annual coupon rate, 15

years to maturity, and a par value of 1,000. The

current price is 928.09. - Will the YTM be more or less than 10?
- MORE
- What is the YTM?
- N 15
- I/Y ???? 11
- PV 928.09
- PMT 100
- FV 1000

The effect of changes in interest rates on bond

prices

- Known as interest rate risk
- Consider two identical 8 coupon bonds except

that one matures in 4 years, the other matures in

10 years - Calculate the change in the price of each bond if

interest rates fall from 8 to 6, if interest

rates rise from 8 to 10

Interest Rates and Time to Maturity

- The longer a bond has till maturity, the greater

the price impact of a change in interest rates - WHY?

Interest Rates and Bond Prices

- Bond Prices and Interest Rates have an Inverse

Relationship

Bond Market Reporting

- Primarily over-the-counter transactions with

dealers connected electronically - Extremely large number of bond issues, but

generally low daily volume in single issues - Makes getting up-to-date prices difficult,

particularly on a small company or municipal

issues - Treasury securities are an exception

Pricing Stocks

- Remember The value of any asset is the present

value of its expected future cash flows. - Bond Cash flows are ________ ________
- Stock produces cash flows from
- ___________
- ___________

Types of Stock

- Preferred stock
- Does not grant voting rights
- Holders receive cash in the form of fixed

dividend payment, or by selling (illiquid) - Common stock
- Grants voting rights to holder
- Cash flow from fluctuating dividends and selling

shares

Stock Valuation Terminology

- Dt or Divt expected dividend at time t
- P0 market price of stock at time 0
- Pt expected price of stock at time t
- g- expected growth rate of dividends
- rs or re- required rate of return on equity
- D1 / P0 expected one-year dividend yield
- (P1 - P0)/ P0 expected one year capital gain
- The stocks total return div yield cap. gain

Valuing Common stock

- The return on a share of stock is
- rs is also known as the capitalization rate
- If the investor requires a return of rs, then the

price he is willing to pay today will depend on

the cash flow he expects to receive _at_ t1

P0 ?

- R
- P1

With Substitution

- This process can be repeated into the future, for

example to period H, so that - Using summation
- P0 ?H Dh / (1 r)h PH / (1 r)H
- What happens to the last term as the time horizon

gets long (as H approaches infinity)

Dividend Valuation model

- As H approaches infinity the last term goes to

zero - Because of this we can value a stock using just

there dividends and an assumption about the

companys growth rate - Dividend Valuation Model- the price of a stock is

equal to the present value of the stream of

expected future dividends

Constant Dividend (No Growth)

- How do you value a stock that will pay a constant

dividend? - Hint what does the cash flow stream look similar

to?

No Growth Example

- What is the value of a share of a firm that is

expected to pay constant dividend of 2 per share

forever? - The required rate of return is 10

Constant Dividend Growth

- If the dividend payments on a stock are expected

to grow at a constant rate, g, and the discount

rate is rs, the value of the stock at time 0

is______, similar to a __________

Constant Growth Example

- Geneva steel just paid a dividend of 2.10.

Dividend payments are expected to grow at a

constant rate of 6. The appropriate discount

rate is 12. What is the price of Geneva stock? - Div1
- P0

Valuation of stocks with variable dividend growth

- Steps
- Find the PV of dividends during the period of

non-constant growth, PA - Find the price of the stock at the end of the

non-constant growth period, PN - Discount the price found in 2 back to the

present, PB - Add the two present values (13) to find the

intrinsic value (price) of the stock P0 PA PB

Generic Differential Growth

- Dividends will grow at g1 for N years and g2

thereafter - Step 1 An N-year annuity growing at rate g1
- Step 2 A growing perpetuity at rate g2
- PN DivN1 / (R-g2)
- Step 3 PB PN / (1R)N
- Step 4 P0 PA PB

Non-Constant Growth Example (Given)

- Websurfers Inc, a new internet firm is expected

to do very well during its initial growth period.

Investors expect its dividends to grow at 25 for

the next 3 years. Obviously one cannot expect

such extraordinary growth to continue forever,

and it is expected that dividends will grow at 5

after year 3 in perpetuity. Its current dividend

is 1/share. Required rate of return on the stock

10. Calculate what the current price should be.

Websurfer Inc, Example (Given)

- PA(11.25)/(0.10-0.25)1-1.25/1.103

3.90 - PN 11.2531.05/(0.10-0.05) 41.00
- PB 41.00/(1.103) 30.80
- P0 PA PB 3.90 30.80 34.70

A Differential Growth Example

- A common stock just paid a dividend of 2. The

dividend is expected to grow at 8 for 3 years,

then it will grow at 4 in perpetuity. - What is the stock worth? The discount rate is 12.

Solution

- PA
- PN
- PB
- P0 PA PB

Important Parameters

- The value of a firm depends on the discount rate,

R, and the growth rate, g.

Market Capitalization Rate

- R is the market consensus of the appropriate

discount rate - This is known as the Market Capitalization Rate
- Return that is expected by an investor buying the

stock today - This is similar to what for a bond?

Where does R come from?

- We generally estimate R from one of the dividend

valuation models - Using constant dividend growth model
- In practice, estimates of R have a lot of

estimation error

Where does R come from?

- What is D1/P0?
- What is g?

Where does R come from?

- What is D1/P0?
- What is g?

Decomposing R

- Stocks are often classified based on this split
- Income/Value stocks have a higher dividend

yield - Growth stocks have a higher growth component
- As long as both are equally risky, the return

should be the same

Where does g come from?

- From analysts' estimates
- I/B/E/S, Google, Yahoo, or WSJ
- From earnings re-investment
- g Retention ratio Return on equity
- How much net income is reinvested in the company

times what the firm can make on the money - This is an estimate of how fast the company can

grow its dividends, which is?

Plowback Ratio

- The portion of a dollar earned that is reinvested

- 1 - Payout Ratio
- 1 - DIV/EPS
- ROE Net Income / Book Equity
- Net Income/ Number of shares
- Book Equity / Number of shares
- EPS / Book Equity per share
- g plowback ratio ROE

Earnings Re-Investment

- g Retained Earnings Net Income
- Net Income Book Equity
- g Plowback Ratio Return on Equity

Link between stock prices and earnings

- A new valuation model
- Consider a firm with a 100 payout ratio, so Div

EPS in each period and earnings remain flat.

Link between stock prices and earnings

- Since the firm is paying out all of its earnings

as dividends, the expected return is simply the

earnings per share divided by the share price

(earnings-price ratio) - r EPS/P0

Present Value of all Future Growth Opportunities

(PVGO)

- The stock price is composed of the value of the

co